6 equal divisions of 31/9 (abbreviated 6ed31/9) is a nonoctave tuning system that divides the interval of 31/9 into 6 equal parts of about 357 ¢ each. Each step represents a frequency ratio of (31/9)1/6, or the 6th root of 31/9.
Intervals
| #
|
Cents
|
Approximate JI ratios (direct)
|
Approximate JI ratios (val)
|
| 1
|
356.9
|
16/13
|
5/4, 6/5, 8/7, 9/8, 7/5, 11/10
|
| 2
|
713.7
|
3/2
|
3/2, 4/3
|
| 3
|
1070.6
|
13/7
|
5/3
|
| 4
|
1427.4
|
16/7
|
2/1
|
| 5
|
1784.3
|
14/5
|
5/2
|
| 6
|
2141.1
|
exact 31/9
|
3/1, 7/2, 11/3
|
Harmonics
| x
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Absolute error (cents)
|
-129
|
-118
|
98
|
69
|
110
|
-157
|
-31
|
121
|
-61
|
131
|
-20
|
| Steps
|
3
|
5
|
7
|
8
|
9
|
9
|
10
|
11
|
11
|
12
|
12
|
| Steps (reduced)
|
3
|
5
|
1
|
2
|
3
|
3
|
4
|
5
|
5
|
0
|
0
|